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pro vyhledávání: '"Kosygina, Elena"'
Autor:
Kosygina, Elena, Yilmaz, Atilla
We establish homogenization for nondegenerate viscous Hamilton-Jacobi equations in one space dimension when the diffusion coefficient $a(x,\omega) > 0$ and the Hamiltonian $H(p,x,\omega)$ are general stationary ergodic processes in $x$. Our result is
Externí odkaz:
http://arxiv.org/abs/2403.15963
Autor:
Kosygina, Elena, Yilmaz, Atilla
We show that, in the periodic homogenization of uniformly elliptic Hamilton-Jacobi equations in any dimension, the effective Hamiltonian does not necessarily inherit the quasiconvexity property (in the momentum variables) of the original Hamiltonian.
Externí odkaz:
http://arxiv.org/abs/2309.09343
We prove homogenization for viscous Hamilton-Jacobi equations with a Hamiltonian of the form $G(p)+V(x,\omega)$ for a wide class of stationary ergodic random media in one space dimension. The momentum part $G(p)$ of the Hamiltonian is a general (nonc
Externí odkaz:
http://arxiv.org/abs/2303.06415
We use generalized Ray-Knight theorems introduced by B\'alint T\'oth in 1996 together with techniques developed for excited random walks as main tools for establishing positive and negative results concerning convergence of some classes of diffusivel
Externí odkaz:
http://arxiv.org/abs/2208.02589
We consider one-dimensional excited random walks (ERWs) with i.i.d. markovian cookie stacks in the non-boundary recurrent regime. We prove that under diffusive scaling such an ERW converges in the standard Skorokhod topology to a multiple of Brownian
Externí odkaz:
http://arxiv.org/abs/2008.06766
Autor:
Davini, Andrea, Kosygina, Elena
Publikováno v:
Journal of Differential Equations, Volume 333, 5 October 2022, Pages 231-267
We prove homogenization for a class of nonconvex (possibly degenerate) viscous Hamilton-Jacobi equations in stationary ergodic random environments in one space dimension. The results concern Hamiltonians of the form $G(p)+V(x,\omega)$, where the nonl
Externí odkaz:
http://arxiv.org/abs/2002.02263
Akademický článek
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Autor:
Davini, Andrea, Kosygina, Elena
Publikováno v:
In Journal of Differential Equations 5 October 2022 333:231-267
Publikováno v:
Communications in Partial Differential Equations (2020), 45:1, 32-56
We prove the homogenization of a class of one-dimensional viscous Hamilton-Jacobi equations with random Hamiltonians that are nonconvex in the gradient variable. Due to the special form of the Hamiltonians, the solutions of these PDEs with linear ini
Externí odkaz:
http://arxiv.org/abs/1710.03087
Autor:
Davini, Andrea, Kosygina, Elena
It was pointed out in [P.L. Lions, G. Papanicolaou, S. Varadhan, Homogenization of Hamilton-Jacobi equation, unpublished preprint (1987)] that, for first order Hamilton-Jacobi (HJ) equations, homogenization starting with affine initial data implies h
Externí odkaz:
http://arxiv.org/abs/1608.01893